One of the tasks when designing radio frequency transmitters is to transmit a signal with a relatively high bandwidth (e.g. 35 MHz) and a relatively high peak-to-average ratio (PAR, e.g. 7 dB) with high power efficiency, good linearity and/or good adjacent channel power ratio (ACPR). The design of the power amplification stage of the transmitter has a large influence on these criteria.
Class AB amplifiers with adaptive digital pre-distortion are able to meet the requirements regarding bandwidth, peak-to-average ratio, linearity and adjacent channel power ratio. However, they do not have a good efficiency. Any kind of linear amplifier (class A, class AB) have low efficiency due high quiescent currents.
The same is basically true for Doherty-amplifiers with adaptive digital pre-distortion.
Two other classes of amplifiers are class E amplifiers and class F amplifiers. Although these types of amplifiers are usually considered very efficient, this is only true for carrier wave signals which have a low PAR. The reason for this is that class E and class F amplifiers are matched to the frequency of the carrier signal.
Polar transmitters, also called envelope-elimination and restoration (EER) transmitters are sufficiently efficient, but their bandwidth and linearity are rather poor. EER transmitters function as follows: An input signal in IQ quadrature representation is converted to polar representation (amplitude and phase). Amplitude and phase data are separated for further processing. Polar transmitters use carrier wave signals to drive class-E or class-F power amplifiers by modulating supply power or power amplifier input signals. To this end, the amplitude data are typically delta-sigma modulated or pulse-width modulated. Modulating the supply voltage of the power amplifier could be done by controlling a DC-to-DC converter in accordance with the modulated amplitude signal. It is also possible to switch the supply voltage between different supply voltages, e.g. VDD, VDD/2, and 0. EER transmitters usually have very limited bandwidth and linearity. Linearity is very sensitive to:                delay mismatch between the amplitude path and the phase path        bandwidth of the amplitude path and the phase path        conversion from amplitude modulation (AM) to pulse modulation (PM).        
EER is non-linear, because 1st and higher order mixing products are created in the process of recombining the phase information and the amplitude information. the following formulas illustrate this.
                              z          ⁡                      (            t            )                          =                ⁢                              a            ⁡                          (              t              )                                ·                      exp            ⁡                          (                              j                ·                                  φ                  ⁡                                      (                    t                    )                                                              )                                                              =                ⁢                              (                                                            a                  wanted                                ⁡                                  (                  t                  )                                            +                                                a                  error                                ⁡                                  (                  t                  )                                                      )                    ·                      exp            ⁡                          (                              j                ·                                  (                                                                                    φ                        wanted                                            ⁡                                              (                        t                        )                                                              +                                                                  φ                        error                                            ⁡                                              (                        t                        )                                                                              )                                            )                                                              =                ⁢                              (                                                            a                  wanted                                ⁡                                  (                  t                  )                                            +                                                a                  error                                ⁡                                  (                  t                  )                                                      )                    ·                      exp            ⁡                          (                              j                ·                                                      φ                    wanted                                    ⁡                                      (                    t                    )                                                              )                                ·                      exp            ⁡                          (                              j                ·                                                      φ                    error                                    ⁡                                      (                    t                    )                                                              )                                                              ≈                ⁢                              (                                                            a                  wanted                                ⁡                                  (                  t                  )                                            +                                                a                  error                                ⁡                                  (                  t                  )                                                      )                    ·                      exp            ⁡                          (                              j                ·                                                      φ                    wanted                                    ⁡                                      (                    t                    )                                                              )                                                                      ⁢                  (                      1            +                          j              ·                                                φ                  error                                ⁡                                  (                  t                  )                                                      -                                          1                2                            ⁢                                                φ                  error                  2                                ⁡                                  (                  t                  )                                                      -            …                    ⁢                                          )                                        =                ⁢                                            z              wanted                        ⁡                          (              t              )                                +                                                    z                wanted                            ⁡                              (                t                )                                      ·            j            ·                                          φ                error                            ⁡                              (                t                )                                              +                                                    a                error                            ⁡                              (                t                )                                      ·                          exp              ⁡                              (                                  j                  ·                                                            φ                      wanted                                        ⁡                                          (                      t                      )                                                                      )                                              +                                                ⁢                                                            a                error                            ⁡                              (                t                )                                      ·                          exp              ⁡                              (                                  j                  ·                                                            φ                      wanted                                        ⁡                                          (                      t                      )                                                                      )                                      ·            j            ·                                          φ                error                            ⁡                              (                t                )                                              +                      …            ⁢                                                  ⁢                                          (                                                                  )                            ·                                                φ                  error                  2                                ⁡                                  (                  t                  )                                                                        wherein z(t) is the input signal, a(t) is the amplitude information and φ(t) is the phase information. As can be seen in the above equation, besides the wanted signal zwanted(t), the 1st order mixing productszwanted(t)·j·φerror(t)+aerror(t)·exp(j·φwanted(t))and the second order mixing productsaerror(t)·exp(j·φwanted(t))·j·φerror(t)+ . . . ( )·φerror2(t)occur. Normal EER treats aerror(t) and φerror(t) separately and cannot correct for 1st and 2nd order mixed errors.
WO 2007/064007 A1, the entire disclosure of which being hereby incorporated by reference into the description, describes an EER transmitter with analogue feedback loops for phase and amplitude. The analogue feedback corrects for distortion, such as compression and AM-PM conversion, that may occur in the power amplifier. However, the problem with separate feedback loops for amplitude and phase is that the complex (I+jQ) signal is a linear function of I and Q, but not of phase and amplitude. Out of band errors of phase and amplitude are noise shaped and therefore have most energy out of band. When the phase and amplitude errors mix with each other due to non-linearities, in-band errors are generated that cannot be corrected. Also, a difference in delay in the amplitude and phase paths cannot be detected with the two loops being separate from each other. The entire disclosure of WO 2007/064007 is hereby incorporated into the description by reference.
U.S. Pat. Nos. 4,929,906 (issued to Voyce, assigned to The Boeing Company), 5,237,288 (issued to Cleveland, assigned to SEA, Inc.), and 5,469,114 (issued to Saxena, assigned to Advanced Milliwave Laboratories) disclose feedback circuits for the linearization of a power amplifier. The '288 patent and the '114 patent disclose a phase correction circuit in the feedback loop. However, none of the three U.S. Pat. No. 4,929,906, U.S. Pat. No. 5,237,288, and U.S. Pat. No. 5,469,114 discloses a delta-sigma modulator or envelope-elimination and restoration. The entire disclosure of the U.S. Pat. No. 4,929,906, U.S. Pat. No. 5,237,288, and U.S. Pat. No. 5,469,114 is hereby incorporated into the description by reference.
U.S. Pat. Nos. 6,256,482 (issued to Raab), 7,068,096 (issued to Chu, assigned to Northrop Grumman Corporation), and 7,400,865 (issued to Järvinen, assigned to Nokia Corporation) disclose EER transmitters. However, none of the three U.S. Pat. No. 6,256,482, U.S. Pat. No. 7,068,096, and U.S. Pat. No. 7,400,865 discloses a delta-sigma modulator. The '096 patent discloses a feedback control loop but this feedback control loop is internal to the EER modulator. The entire disclosure of the U.S. Pat. No. 6,256,482, U.S. Pat. No. 7,068,096, and U.S. Pat. No. 7,400,865 is hereby incorporated into the description by reference.